Controlled-source electromagnetic (“CSEM”) surveys are an important geophysical tool for evaluating the presence of hydrocarbon-bearing strata within the earth. CSEM surveys typically record the electromagnetic signal induced in the earth by a source (transmitter) and measured at one or more receivers. The behavior of this signal as a function of transmitter location, frequency, and separation (offset) between transmitter and receiver can be diagnostic of rock properties associated with the presence or absence of hydrocarbons. A notable diagnostic rock property of this kind is electrical resistivity. Thus, CSEM measurements are typically used to determine the spatially-varying resistivity of the subsurface.
In the marine environment, CSEM data are typically acquired by towing an electric dipole transmitting antenna 10 among a number of receivers 11 positioned on the seafloor 12 (FIG. 1). The receivers typically have multiple sensors designed to record different vector components of the electric and/or magnetic fields. The transmitter antenna is typically towed (by a vessel on the sea surface 13) a few tens of meters above the seafloor. The receivers are weighted and fall to the seafloor, but release their weight and rise back to the surface with the data after receiving an acoustic command from the ship. Alternative configurations include stationary transmitters on the seafloor or in the water column as well as magnetic transmitter antennae. The transmitting and receiving systems typically operate independently (without any connection between them), so that receiver data must synchronized with shipboard measurements of transmitter position by comparing clock times on the receivers to time from a shipboard or GPS (Global Positioning System) standard.
CSEM data are typically interpreted in the temporal frequency domain, each signal representing the response of the earth to electromagnetic energy at that temporal frequency. Temporal frequency domain means the data is transformed, typically by Fourier transformation, such that the dependence of the data on time becomes dependence on frequency. In raw data, the strength of each frequency component varies depending on how much energy the transmitter broadcasts (i.e., the amplitude of each component in the transmitter's frequency spectrum) and on the receiver sensitivity at that frequency. These transmitter and receiver effects are typically removed from the data prior to interpretation. FIGS. 2A-B depict raw receiver data 21 together with the transmitter waveform 22 that gave rise to it. FIG. 2A displays measured data on a time scale of several hours while FIG. 2B shows the received signal (and, for reference, the transmitted signal) on a much shorter time scale, comparable to the transmitter signal period, typically between 4 and 32 seconds. (The vertical scale applies only to the receiver signal.)
In practice, the receiver data are usually converted to temporal frequency by dividing (or “binning”) the recorded time-domain data into time intervals (x1, x2, and x3 in FIG. 3A) equal to the transmitter waveform period (FIG. 3A) and determining the spectrum within each bin by standard methods based on the Fourier transform (FIG. 3B). (The phases of the spectral components are not shown.) With each bin is associated a time, typically the Julian date at the center of the bin. Since the transmitter location is known as a function of time, these bins may be interchangeably labeled in several different ways: by Julian date of the bin center; by transmitter position; by the signed offset distance between source and receiver; or, by the cumulative distance traveled by the transmitter relative to some arbitrarily chosen starting point.
In general, the received signals are made up of components both in-phase and out-of-phase with the transmitter signal. The signals are therefore conveniently represented as complex numbers in either rectangular (real-imaginary) or polar (amplitude-phase) form.
The transmitter signal may be a more complex waveform than that depicted in FIGS. 2B and 3A.
The magnitude of the measured electric field falls off rapidly with increasing source-receiver offset (FIG. 4A). When the offset is large enough, the earth's response to the transmitted signal will be weak and the measured signal will be corrupted by noise. Noise is a limiting factor in applying CSEM surveys to hydrocarbon exploration because it obscures the response from subtle earth structures, interferes with the use of data from multiple receivers, and restricts the range of temporal frequencies that can be used.
While some types of noise can be overcome by increasing transmitter strength or slowing the speed of the survey vessel, both approaches are costly. It is therefore advantageous to use computer-based signal processing techniques to mitigate noise in CSEM data.
When the origin of the noise is known precisely, it can sometimes be removed by explicit modeling and subtraction, as PCT Patent Publication No. WO2005/010320 published on Feb. 3, 2005, discloses for the case of air-wave noise. In other cases, where the origin of the noise is less well understood or where it may originate in more than one phenomenon, suppression methods can be based on how the noise presents itself in the data. For example, PCT Patent Publication No. WO2006/088591 published on Aug. 24, 2006, describes a method where noise is estimated from signals measured at frequencies that were not transmitted by the source.
FIGS. 4A and 4B depict electric-field data (amplitude data in FIG. 4A, phase data in FIG. 4B) containing noise that can be mitigated by this invention. The vertical axis in FIG. 4A is magnitude of the electric field normalized by the transmitter strength. The transmitter traveled about 59 km during the 0.9 days covered by the horizontal axis. The transmitter approaches the receiver from the left, passes nearest to the receiver at about day 184.95, and recedes from the receiver to the right. Each data point represents the electric field amplitude at 0.0625 Hz. computed from a 32-second bin which is equivalent to about 24 meters of transmitter movement for this survey. The large signal fluctuations before day 184.85 and after day 185.51 cannot be physically attributed to variations in the subsurface resistivity, which is unchanging over such short time intervals. These fluctuations can only be noise.
The location of the transmitter antenna 10 as a function of time is recorded during the course of the CSEM survey. As a result, there is no confusion regardless of whether the CSEM data are considered as a function of time, as is the case for the horizontal axis shown in FIGS. 4A-B, or as a function of source-receiver offset. In either view, fluctuations which occur too rapidly (in either offset or time) may be properly considered to be noise. Although offset is more commonly used as the independent variable, time is a more convenient choice in the case where the transmitter antenna is held at a fixed location for an extended period of time. In particular, when the transmitter antenna is held fixed, it may be desirable to remove rapidly-varying noise by means of the present invention prior to assigning an offset to the data.
Those skilled in the art of digital signal processing will know of techniques that will decompose time series, such as raw CSEM data, to temporal frequency without explicitly dividing the data into non-overlapping time intervals. In general, a time series may be transformed to the time-frequency domain and the dominant temporal frequencies extracted separately as functions of time. Some methods of transforming data to the time-frequency domain include the Short-Time Fourier Transform (J. Allen, L. Rabiner, “A Unified Approach to Short-Time Fourier Analysis and Synthesis,” Proc. of the IEEE 65, 1558-64 (1977)); the Wavelet Transform (W. C. Lang and K. Forinash, “Time-frequency analysis with the continous wavelet transform,” Am. J. Phys. 66, 794-797 (1998)); the Wigner-Ville transform (E. Wigner, On the quantum correction for thermodynamic equilibrium, Phys. Rev. 40, 749-759 (1932), and J. Ville, “Theorie et application de la notion de signal analytique,” Cables et Transmission, 2A., 61-74 (1948)); the Choi-Williams transform (H. Choi and W. Williams, “Improved time-frequency representation of multicomponent signals using exponential kernels,” IEEE Trans. on Acoust., Speech, and Signal Processing 37, 862-871 (1989)); and the Bessel method (Z. Guo, L. G. Durand, and H. C. Lee, “The time-frequency distributions of nonstationary signals based on a Bessel kernel,” IEEE Trans. on Signal Proc. 42, 1700-1707 (1994)). The present invention is not limited to any particular method or methods for spectral decomposition of CSEM data to the temporal frequency domain.
The decomposition to temporal frequency indicated in FIG. 3B is itself a noise-rejection method since it suppresses those portions of the signal that do not correspond to frequencies that were broadcast by the transmitter.
A direct approach to mitigating rapidly-varying noise is to “stack” the data by combining several adjacent time bins into a single, larger bin. See, for example, L. M. MacGregor et al., “The RAMESSES Experiment-III. Controlled-source Electromagnetic Sounding of the Reykjanes Ridge at 57° 45′ N,” Geophys. J. Int. 135, 773-789 (1998). The use of weighted stacks has been discussed by Macnae, et al. for time-domain surveys (Geophysics 49, 934-948 (1984)).
Mitsuhata et al. (“The Fourier Transform of Controlled-Source Time-Domain Electromagnetic Data by Smooth Spectrum Inversion,” Geophys. J. Int. 144, 123-135 (2001)) teach a method to estimate the Fourier transform of time domain data using least-squares inversion with a smoothness constraint. An objective is to compute at logarithmically-spaced values the frequency spectrum of time-domain measurements. The authors assume that the frequency-domain amplitudes and phases are smoothly varying with errors stemming from noise in the time-domain data. They further assume that both these errors and the errors in the original data follow Gaussian distributions whose widths are characterized by parameters they refer to as hyperparameters. Accordingly, they perform a least-squares fit of the measurements to sine and cosine waveforms at the logarithmically-spaced frequencies, at the same time fitting the constraints imposed by causality (that the measurements may not occur in time prior to the signal that generates them) and fitting the Gaussian distribution assumptions. As a final step, the hyperparameters are adjusted to minimize the error in these fits.
Spies estimates the noise on one component of the magnetic field from measurements on the other two components (Geophysics 53, 1068-1079 (1988)).
Spatial filters have been applied to reduce noise in aeromagnetic data, which are airborne measurements of the naturally occurring, static (zero-frequency) magnetic field of the earth. See, for example, B. K. Bhattacharyya, “Design of spatial filters and their application to high-resolution aeromagnetic data,” Geophysics 37, 68-91 (1972).
The behavior and origin of noise in marine CSEM surveys can vary significantly from place-to-place in the earth and with changes in ocean currents and atmospheric conditions. Moreover, the noises in any particular CSEM data set may stem from more than one source and exhibit more than one type of behavior. It is therefore desirable that any CSEM noise suppression technique can be applied together with other noise-rejection techniques, such as decomposition to temporal frequency and stacking.
Stacking is a statistical process is most effective when the noise has a Gaussian distribution about some mean value. In marine CSEM data, the noise can have very large excursions from its mean value. As a result, larger stacking bins will tend to be dominated by a few of the largest noise spikes and can fail to represent the underlying signal. In addition, large stacking bins decrease the spatial resolution of the data, since it becomes unclear how large bins should be associated with a specific time or offset. Spatial resolution is important since the user of CSEM data is attempting to determine both the resistive nature and position of strata in the subsurface.
On land, most noise-suppression methods deal only with data acquired during time periods when the transmitter current is off. This strategy is crucial for land data since it provides a way of rejecting the very large signal that reaches the receiver through air (the “air wave”). The air wave is typically rejected by restricting the data analysis to time intervals where no energy is traveling through the air. In some land surveys and all marine surveys, data are acquired in the time domain, but the source consists of a repetitive waveform such as that shown in FIG. 2. Such repetitive waveforms are dominated by a small number of frequencies (perhaps 10, but as few as one) and are typically analyzed by binning the data at the waveform period and then transforming the data within each bin to frequency—as outlined above. In the marine setting, the air-wave is often suppressed by ohmic losses in the water. In addition, by keeping the transmitter mostly in an “on” state, marine surveys can operate at increased signal levels and spread more energy out among different temporal frequencies to better resolve the earth's structure in depth.